\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(\frac{B}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.4}\)

\(\frac{B}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-...+\frac{1}{15}-\frac{1}{28}\)

\(\frac{B}{7}=\frac{1}{2}-\frac{1}{28}\)

\(\frac{B}{7}=\frac{13}{28}\)

\(B=\frac{13}{28}.7\)

\(B=\frac{13}{4}\)

\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(\frac{B}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.4}\)

\(\frac{B}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{15}-\frac{1}{28}\)

\(\frac{B}{7}=\frac{1}{2}-\frac{1}{28}\)

\(\frac{B}{7}=\frac{13}{28}\)

\(B=\frac{13}{28}.7=\frac{13}{4}\)

\(n=7\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\)

\(tacocongthuc:\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\)

\(\Rightarrow n=7\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-.....-\frac{1}{28}\right)=7\left(\frac{1}{2}-\frac{1}{28}\right)=\frac{7.13}{28}=\frac{13}{4}\)

#)Giải :

( k chép lại đề )

\(\frac{n}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.4}\)

\(\frac{n}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{15}-\frac{1}{28}\)

\(\frac{n}{7}=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)

\(\Rightarrow n=\frac{13}{28}.7=\frac{13}{4}\)

Câu a:

(4\(\frac{5}{37}\) - 3\(\frac45\) + 8\(\frac{15}{29}\)) - (3\(\frac{5}{37}\) - 6\(\frac{14}{29}\))

= 4\(\frac{5}{37}\) - 3\(\frac45\) + 8\(\frac{15}{29}\) - 3\(\frac{15}{37}\) + 6\(\frac{14}{29}\)

= (4 - 3) + (\(\frac{5}{37}-\frac{5}{37}\)) + (8 + 6) + (\(\frac{15}{29}\) + \(\frac{14}{29}\)) - 3 - \(\frac45\)

= 1 + 0 + 14 + 1 - 3 - \(\frac45\)

= 1 + 14 + 1 - 3 - \(\frac45\)

= 15 + 1 - 3 - \(\frac45\)

= 16 - 3 - \(\frac45\)

= 13 - \(\frac45\)

= \(\frac{61}{5}\)